Question: Simplify the following expression: $ q = -10 + \dfrac{-5}{r - 7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r - 7}{r - 7}$ $ \dfrac{-10}{1} \times \dfrac{r - 7}{r - 7} = \dfrac{-10r + 70}{r - 7} $ Therefore $ q = \dfrac{-10r + 70}{r - 7} + \dfrac{-5}{r - 7} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-10r + 70 - 5}{r - 7} $ $q = \dfrac{-10r + 65}{r - 7}$